Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
from bisect import bisect_left

def BinarySearch(a, x):
    i = bisect_left(a, x)
    if i != len(a) and a[i] == x:
        return i
    else:
        return -1

n=int(input())
possible_nums = []
i=1
a = 0
while a<=n:
    a = (math.pow(i,2)+i)/2
    if(a<=n):
        possible_nums.append(a)
    i+=1
possible = 0
for a in possible_nums:
    diff = n-a
    i = BinarySearch(possible_nums,diff)
    if i>=0:
        print("YES")
        possible = 1
        break
    else:
        continue
if not possible:
    print("NO")